Baking object with "combined" results in much too bright an Image Texture (Cycles)
I can't be sure, but it seems entirely likely that your whites are getting crushed. I can guarantee that the white in your specular highlight on that chair is much higher than "255." But a typical image can only hold up to a 255.

Generically, this situation is handled one of two ways. Either, anything over 255 is just clipped/clamped to 255, or the whole range of values is crushed/scaled so that everything fits in a 0-255 range. This makes all the highlights darker because what used to be between 1000-2000 level of intensity gets scaled down to something like 150-250.

You situation would only be explained if Blender is doing some kind of intensity compensation that's tuning everything down so that your whites are crushed instead of just clipped. I don't know if Blender actually does that or not, but it'd explain what you're seeing.

I also don't know how to solve that, unless you can bake to an EXR or HDR that will record values higher than 255.

Hope that helps.